Heretofore, for semiconductor manufacturing facilities and at chemical plants, a differential pressure flowmeter and the like such as a mass flow type flowmeter (a thermal type mass flow meter) and the like and a buildup type flowmeter and the like have been widely used to measure or control a flow rate of process gases, raw material gases and the like.
However, with a thermal type mass flowmeter and the like, there have been seen a number of difficulties such as a low responsivity, a poor measuring accuracy in a small flow quantity range, a large number of operational problems, a limited variety of gases subject to control, and being easily influenced by pressure changes and the like.
Similarly, with a buildup type flowmeter and the like, there have been seen some difficulties such as being difficult in measuring or controlling a flow rate in real time, not being able to use in a state of inline, an existence of restraints of a pressure of gases subject to control, a separate line required for measurements and the like.
On the other hand, a differential pressure type flowmeter and the like for which an orifice and a manometer are employed demonstrates excellent effects such as having nearly no restraints of the type of gases subject to control, being usable in a state of incline, and also measuring and controlling a flow rate being able to be performed in real time.
However, this type of a differential pressure type flowmeter and the like uses an equation for a flow rate computation derived from Bernoulli's theorem with the assumption that the fluid is non-compressible, and then the flow rate of the fluid is computed by giving some corrections to it. Therefore, if large pressure changes of the fluid arise (that is, when approximations that the fluid is non-compressible break), a substantial drop in accuracy of measuring and controlling a flow rate cannot be avoided, thus resulting in a failure of accurate flow rate measurements and controls.
To solve these difficulties with the aforementioned differential pressure type flowmeter and the like, a pressure type flowmeter and the like has been developed and disclosed (TOKU-KAI-HEI No. 10-55218 and others) wherewith critical conditions of a fluid passing through an orifice, that is, a pressure P1 on the upstream side of an orifice and a pressure P2 on the downstream side of an orifice being forcibly set to make the velocity of a fluid to be the velocity of sound, and the flow rate of a liquid Q is computed by the theoretical equation Q=KP1 under the critical conditions.
However, even with the pressure type flowmeter and the like, non-critical conditions occur when a fluid is in a small flow quantity range (that is, when a pressure P1 on the upstream side of an orifice and a pressure P2 on the downstream side to an orifice are in a state of being close), thus resulting in large errors in a flow rate measurement value Q or a flow rate control value Q.
Namely, with a conventional differential pressure flowmeter (or a pressure type flowmeter) and the like, it is so made that an equation for a flow rate computation derived from Bernoulli's theorem with the assumption that a fluid is non-compressible is used, and under non-critical conditions before a fluid reaches the velocity of sound (a non-sound velocity range), a flow rate on the downstream side is determined by the equationQc=SC(P2(P1−P2))1/2/T1/2,where under critical conditions after having reached the velocity of sound (a sound velocity range), a flow rate Q is computed by an equationQc=SCP1/T1/2(where T is an absolute temperature of a fluid passing through an orifice, S is a cross-sectional area of an orifice and C is a proportional factor).
Critical conditions for the velocity of a fluid to reach the velocity of sound is given by a critical value rc of a pressure ratio P2/P1. The critical value rc is determined by the equationP2/P1=rc=(2//(n+1))n/(n−1) using a specific heat ratio n of a gas.
Furthermore, a specific heat ratio n is given by the equationn=Cp/Cv where Cp is a constant pressure specific heat and Cv is a constant volume specific heat. With biatom-molecular gases, n isn=7/5=1.4,and rc is Rc=0.53, while with non-linear type triatom-molecular gases, n isn=8/6=1.33,and rc is Rc=0.54.
To solve problems with the aforementioned conventional differential pressure type flowmeter (or a pressure type flowmeter), a flow rate value computed with the previous theoretical flow rate equation derived from the assumption that a fluid to be used under non-critical conditions is non-compressible is compared with the actually measured flow rate value, to derive an empirical flow rate equation having a plurality of parametersQc′=SC/T1/2·P2m(P1−P2)n=KP2m(P1−P2)n from a previous theoretical flow rate equationQc=SC/T1/2(P2(P1−P2))1/2,and to determine the aforementioned parameters m and n to make a flow rate value computed by the empirical flow rate equation Qc′ equal to a measured value, thus an empirical flow rate equation Qc′ that suitably matches with the fluid of compressibility being introduced by inventors of the present invention, and disclosed in TOKU-GAN No. 2001-399433.
With the aforementioned empirical flow rate equation Qc′, a proportional constant K is given by SC/T1/2 and computed from conditions of substance and absolute temperature T. P1 designates a pressure on the upstream side of an orifice and P2 a pressure on the downstream side of an orifice. kPaA (kilo Pascal Absolute pressure) is the unit. Further, in the measured flow rate range of 10-30 sccm (a unit of a flow rate in a normal state), it has been found that parameters m and n are m=0.47152 and n=0.59492 respectively.
The values of the aforementioned 2 parameters m and n have a dependence on the range of a flow rate to be measured and the type of a gas. The aforementioned values m=0.4715 and n=0.59492 are values that hold true when the flow rate is in the range of 10-30 sccm. So, m and n don't hold true when the range of a flow rate is 10-100 sccm or 100-1000 sccm, and accordingly they deviate from these values.
FIG. 14 is a block diagram of an improved pressure flow controller for which the aforementioned empirical flow rate equation Qc′. This was previously disclosed by inventors of the present invention in the TOKU-GAN No. 2001-399433. The controller in the FIG. 14 is constituted as a flow controller. However, it is easily understood that it can be turned to be a differential pressure type flowmeter by eliminating a control valve 21, a valve driving part 22, and a flow rate comparison part 23e. 
Referring to FIG. 14, 20 designates an orifice, 21 designates a control valve, 22 designates a valve driving part, 23 designates a control circuit, 23a designates a pressure ratio computation part, 23b designates a pressure ration computation part, 23c designates a flow rate computation part, 23d designates a flow rate computation part, 23e designates a flow rate comparison part, P1 designates a fluid pressure detector on the upstream side of an orifice, P2 designates a fluid pressure detector on the downstream side of an orifice, T designates a fluid temperature detector, Qs designates a flow rate setting value signal, ΔQ designates a flow rate difference signal, and Qc′ designates a flow rate computation value.
With the controller, firstly a pressure ratio P2/P1 is computed with the detected upstream side pressure P1 and downstream side pressure P2 (23a), a judgment is made continually to find if the fluid is under critical conditions or non-critical conditions (23b), and the flow rate is computed with a flow rate equation Qc=KP when under critical conditions (23c), while the flow rate is computed with an empirical flow rate equationQc′=KP2m(P1−P2)n when under non-critical conditions.
As stated above, the value of critically rc is given by an equation (2/(n+1))n/(n−1), (where n is the specific heat ratio of a gas). With bi-atom molecular gases, rc is rc=0.53 and with non-linear tri-atom molecular gases, rc is rc=0.54. Therefore, rc is written as rc=approx. 0.5.
A flow rate difference ΔQ between a set flow rate Qs and a computed flow rate Qc is computed with a flow rate comparison part 23e to operate a valve driving part 22 to control valve 21 so that the flow rate difference ΔQ reaches zero. However, when it is used as a flow meter, as stated above, a flow rate comparison part 23e, a control valve 21 and a valve driving part 22 can be eliminated.
Curve A in FIG. 15 shows flow rate measurements or flow rate control characteristics with an improved pressure type flowmeter and the like, while Curve B shows flow rate measurements or flow rate control characteristics with an conventional pressure type flowmeter and the like when an equation Qc=KP1 is used under non-critical conditions. As apparent from FIG. 15, with the improved pressure type flowmeter and the like, a flow rate equation Qc=KP1 is used when under critical conditions, while an empirical flow rate equationQc′=KP2m(P1−P2)n is used when under non-critical conditions, thus an accurate flow rate Q in proportion to the set flow rate being able to be computed, linearity to a set % of a flow rate being held as shown by Curve A in FIG. 15, and the comparatively accurate flow rate measurement and control being ensured even in the range of a small flow quantity.
Patent Literature 1: TOKU-KOU-SHO No. 59-19365 Public Bulletin
Patent Literature 2: TOKU-KOU-SHO No. 59-19366 Public Bulletin
Patent Literature 3: TOKU-KAI-HEI No. 10-55218 Public Bulletin